Abstract
We introduce Neural Particle Automata (NPA), a Lagrangian generalization of Neural Cellular Automata (NCA) from static lattices to dynamic particle systems. Unlike classical Eulerian NCA where cells are pinned to pixels or voxels, NPA model each cell as a particle with a continuous position and internal state, both updated by a shared, learnable neural rule. This particle-based formulation yields clear individuation of cells, allows heterogeneous dynamics, and concentrates computation only on regions where activity is present. At the same time, particle systems pose challenges: neighborhoods are dynamic, and a naive implementation of local interactions scale quadratically with the number of particles. We address these challenges by replacing grid-based neighborhood perception with differentiable Smoothed Particle Hydrodynamics (SPH) operators backed by memory-efficient, CUDA-accelerated kernels, enabling scalable end-to-end training. Across tasks including morphogenesis, point-cloud classification, and particle-based texture synthesis, we show that NPA retain key NCA behaviors such as robustness and self-regeneration, while enabling new behaviors specific to particle systems. Together, these results position NPA as a compact neural model for learning self-organizing particle dynamics.
Abstract (translated)
我们介绍了一种名为神经粒子自动机（Neural Particle Automata，NPA）的新模型，它是对静态格点系统中的神经细胞自动机（Neural Cellular Automata，NCA）进行拉格朗日泛化的动态粒子系统的扩展。与经典欧拉方法下的NCA不同，在这种情况下，每个单元被固定在像素或体素上，NPA将每个单元视为具有连续位置和内部状态的粒子，这两个参数都通过一个共享且可学习的神经规则更新。基于粒子的这一形式化方法清晰地界定了各细胞个体性，允许异质动态，并仅对存在活动的区域进行计算。 然而，粒子系统也带来了一些挑战：邻居关系是动态变化的，直接实现局部相互作用会导致其复杂度随粒子数量呈二次增长。为了解决这些问题，我们用可微分的光滑粒子流体动力学（Smoothed Particle Hydrodynamics，SPH）算子替代了网格感知方法，并且利用内存高效、CUDA加速的核心进行支持，从而实现了端到端的大规模训练。 在包括形态发生、点云分类和基于粒子的纹理合成等任务中，我们展示了NPA不仅保留了NCA的关键特性（如鲁棒性和自我再生），而且还赋予粒子系统特有的新行为。综上所述，这些结果将NPA定位为一种紧凑型神经模型，用于学习自组织的粒子动力学。
URL
https://arxiv.org/abs/2601.16096
